Question: Solve for $y$. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. $-65y+19 < -2y + 41$
Solution: $\begin{aligned}-65y+19 & < -2y + 41 \\\\ -65y&< -2y+22 &(\text{Subtract } 19 \text{ from both sides}) \\\\ -63y &< 22 &(\text{Add } 2y \text{ to both sides})\\\\ 63y&> -22&(\text{Multiply both sides by }-1)\\\\ y&>-\dfrac{22}{63}&(\text{Divide both sides by }63) \end{aligned}$ [Why did the inequality sign flip when we multiplied by -1?] In conclusion, the answer is $y >- \dfrac{22}{63}$.